Why high-degree polynomials can lead to mathematical disaster
In this Stand-up Maths presentation, mathematician Matt Parker explores the Runge phenomenon. Discover why increasing the complexity of a mathematical model can unexpectedly cause wild, unstable oscillations known as Runge spikes.
The video examines the Runge phenomenon, a specific type of instability that occurs when using high-degree polynomials for interpolation. While it might seem intuitive that a more complex polynomial would provide a more accurate fit for a set of data points, these 'Runge spikes' demonstrate how the method can instead produce extreme errors at the edges of an interval.
Source: Beware the Runge Spikes!
